## Symmetry

Some 2D shapes have **lines of symmetry** and **rotational symmetry**.

**Line of symmetry** – This is a line that you can draw through a shape such that what you see on one side of that line is a “mirror-image” of what you see on the other side.

**Rotational symmetry** – The order of rotational symmetry of a shape is the number of times the shape can be rotated and still look the same.

You should be happy with the following topics before vising symmetry:

– 2D Shapes and Quadrilaterals

## Lines of Symmetry in Regular Polygons

Below are a selection of common shapes with their **lines of symmetry** shown as **red, dashed lines**.

The number of **lines of symmetry** in a** regular polygon** is equal to the number of sides.

## Rotational symmetry

The order of **rotational symmetry** of a shape is the number of times the shape can be rotated and still look the same.

The pentagon below can be rotated 5 times and look the same.

This means it has **rotational symmetry order 5**.

If a shape can be rotated 360\degree and only looks the same when it is back at its original position, then it has **rotational symmetry order 1.**

The **rotational symmetry** and **lines of symmetry** of common shapes is shown below.

## Irregular polygons

Many shapes have **no lines of symmetry** at all, like the triangle shown below.

So, we can conclude that some triangles are symmetrical whilst others are not.

The trapezium on the left has 1 line of symmetry, whilst the trapezium on the right has none.

There’s no need to try to memorise all of these shapes and their **lines of symmetry**. Instead, get used to what a shape looks like when it is symmetrical.

### Take an Online Exam

#### Symmetry Online Exam

### Example Questions

**Question 1:** State the number of lines of symmetry an **equilateral** triangle has:

**[1 mark]**

Looking at the picture we can see an equilateral triangle has **three** lines of symmetry, each one from a vertex to the centre of the opposing side,

**Question 2:** State the number of lines of symmetry an **isosceles** triangle has:

**[1 mark]**

Looking at the picture we can see an isosceles triangle only has **one** line of symmetry, a vertical line from top to bottom.

**Question 3:** Below is a regular pentagon. Draw all lines of symmetry on the shape

**[1 mark]**

If we recall, a regular pentagon should have 5 lines of symmetry since it has 5 sides. Drawing all 5 lines on, we get the picture below:

**Question 4:** Draw a shape with exactly 2 lines of symmetry. Include the lines of symmetry on your drawing.

**[1 mark]**

There are a number of possible shapes you could make with two lines of symmetry, the most straightforward being a rectangle.

**Question 5:** Draw all lines of symmetry on the shape below.

**[1 mark]**

The shape has 8 lines of symmetry .

### Worksheets and Exam Questions

#### (NEW) Symmetry Exam Style Questions - MME

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